The search for silver linings in the murky cloud of yesterday's Israeli election requires a great effort of the will. There is not much to go on. You could draw comfort from the fact that Likud's Bibi Netanyahu, who thought he was such a dead cert to win a matter of weeks ago, was rejected, albeit narrowly, in favour of the woman he so consistently patronised, Tzipi Livni of Kadima.

Or you might take solace in the notion that the near tie between Bibi and Tzipi would most easily be resolved by the pair rotating the premiership between them, each taking a two-year turn, following the precedent set by Shimon Peres and Yitzhak Shamir after they fought each other to a dead heat in 1984. The virtue of such an arrangement could be the exclusion of the ultra-nationalist hardman Avigdor Lieberman, whose Israel Beytenu – Israel our Home – party surged to third place on Tuesday.

Or you might assume that the likeliest coalition will be unambiguously of the right, given that – even though Likud itself fell short – the parties of the self-styled "national camp" won a convincing victory over the centre-left bloc. Bibi's motivation will be to expose Kadima to the chill of opposition for the first time in its short life, where, Bibi hopes, it will wither and die. The result will be the most rightwing government in Israel's history. Good, one longtime peace campaigner told me yesterday. "Let the right have power and live with the consequences." They will soon be on a collision course with Barack Obama's Washington. Under US pressure, they will unravel, the right's limitations will have been exposed and the pendulum will swing back leftwards.

Even if that is too hopeful, some on the Israeli left see a value in the country having a full-bloodedly rightist government. "Maybe we're like the alcoholic who needs to touch bottom before we can start the climb back up," was how one put it. Perhaps there has to be a crisis before there can be a recovery.

If these sound like heroic attempts at self-consolation, that is because they are. The truth is, the clouds are much clearer to see. The hawkish camp thumped the centre left on Tuesday, and that's even when you generously count Kadima and Labour – co-authors of operation Cast Lead – as the centre left. But this is about more than a victory for the right. Something else happened and its face belongs to Avigdor Lieberman, the kingmaker whose 15 seats are essential if either Bibi or Livni are to govern without each other.

He does not fit straightforwardly on the Israeli right wing. For one thing, he is avowedly secular. Indeed, much of his appeal was to anti-religious voters who liked his demand for civil unions, thereby breaking the orthodox rabbinate's current monopoly on state-sanctioned marriage. Talk of liberalising the sale of pork products proved too much for at least one religious party, whose spiritual leader warned that a vote for Lieberman was a vote for Satan. The result is that Bibi may find assembling a coalition that includes both the religious parties and Lieberman impossible.

Even more striking is the kingmaker's stance on the defining issue of Israeli politics: territorial compromise. The hard right have always opposed the very idea, clinging to the notion of Greater Israel. But Lieberman – who lives in a West Bank settlement – has said he would be prepared to give up even his own home. Unlike some of his fellow settlers, he does not regard the land as sacred soil that can never be conceded.

Make no mistake, this is not because Lieberman is some kind of crypto- ­peacenik. The opposite is true: I saw him give a victory speech on Tuesday in which he declared his refusal to join any government that would allow Hamas to remain in power: "Our first goal is clear, to destroy Hamas, to take it down."

What separates Lieberman from the traditional Revisionist Zionists that formed Likud is that his goal is not holding on to the maximum amount of land but governing over the minimum number of Arabs. To put it concisely, he would prefer a smaller, ethnically pure Israel to a larger, binational one. To that end, he would give up heavily-populated Palestinian areas of the West Bank and – much more controversially – seeks to redraw the border so that Arab areas of pre-1967 Israel become part of a Palestinian state. In other words, those who are now Palestinian citizens of Israel will find themselves living in their same homes – but under the jurisdiction of another country. Whether their consent will be sought for this move is left vague.

But it's not this idea which has made Lieberman such a toxic force. For that you have to look to the slogan that drove his campaign: "No loyalty, no citizenship." He would insist that every Israeli swear an oath of loyalty to Israel as a Jewish state: anyone who refuses will lose his citizenship.

Israel Beytenu denies this is racist, insisting that every Israeli will have to swear the oath, Jewish or Arab. It is true that plenty of ultra-orthodox Jews who don't accept the authority of a godless secular state may also refuse. But the target is clearly Israel's 1.45 million Arabs. If they will not swear their allegiance, explains Lieberman deputy Uzi Landau, "They will have residency rights but no right to vote or be in the Knesset."

It is a truly shocking idea. I asked several Israel Beytenu luminaries if they could name a single democracy anywhere that had removed citizenship from those who already had it. I asked what they would make of demanding that, say, British Jews, swear an oath of loyalty to Britain as a Christian country on pain of losing their right to vote. I got no good answers.

There was a time when such a poisonous idea would have been confined to the lunatic extremes of the racist Kach party, led by Meir Kahane (of whose youth wing Lieberman was once a member). Twenty five years ago Kahane was banned from the Knesset. Now his heir is courted by the two main parties, desperate for his support. Kadima is untroubled by the loyalty oath scheme; Bibi says he agrees with it.

Who is to blame for this? Israel Beytenu puts the blame on the Israeli Arab leadership for flaunting their "disloyalty", especially during January's Gaza offensive when several prominent Israeli Arabs proclaimed their solidarity with Hamas. They say no democratic society could tolerate such a fifth column, cheering on a mortal enemy.

The Israeli left bear some indirect responsibility here too, at least for the idea of reassigning Palestinian villages inside Israel to Palestine. For years, the left has couched its opposition to the occupation in demographic terms: ruling over millions of Palestinians would eventually imperil Israel's status as a Jewish state. Lieberman is simply extending that logic beyond the 1967 borders. In this sense Lieberman is the bastard child of the Israeli peace movement.

Above all, it is Israeli society that has to take a hard look at itself. For so long, it has lived inside a bubble in which it can only see its side of the story: they hit us, so we hit back; we are under siege from hostile forces, we are the victim. In this mental landscape, even a Moldovan-born immigrant stripping people born in their own land of their citizenship can come to seem acceptable. What's needed is not just a change in the electoral system that would allow "strong government" of the kind Lieberman yearns to implement. What's needed is for Israelis to step outside the bubble, to begin to see the causes of their current predicament, instead of dealing again and again, ever more ineffectively, with the symptoms. Tuesday's election prompts no confidence that that is about to happen.